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302.6. A creatures activated ability with the tap symbol or the untap symbol in its activation cost cant be activated unless the creature has been under its controllers control continuously since his or her most recent turn began. A creature cant attack unless it has been under its controllers control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.

In short: Summoning Sickness means a creature can't attack, or activate abilities with a tap or untap symbol in their cost, until they've been under your control since your untap step.

If a permanent on the battlefield is turned into a creature — e.g. you transform your Mutavault — it will suddenly start being affected by summoning sickness, if you haven't controlled that permanent since the beginning of your turn. For this reason, an alternate way to describe it is that everything has summoning sickness, but it only affects things if they're creatures.

Creatures affected by summoning sickness can still be tapped by other things, though. You can cast Devout Invocation, for instance, and tap a creature that you only just summoned.

As a side note, if Elspeth were to somehow become a creature (by a combination of Mycosynth Lattice and March of the Machines, for example), she would have summoning sickness. You would still be able to activate her abilities, because they don't require tapping, but you wouldn't be able to attack with her the turn you played her.
– murgatroid99♦Jul 4 '14 at 14:11